Stirred tank mass transfer

In many types of contactors, such as stirred tanks, rotary agitated columns, and pulsed columns, mechanical energy is appHed externally in order to reduce the drop si2e far below the values estimated from equations 36 and 37 and thereby increase the rate of mass transfer. The theory of local isotropic turbulence can be appHed to the breakup of a large drop into smaller ones (66), resulting in an expression of the form... 

Over 25 years ago the coking factor of the radiant coil was empirically correlated to operating conditions (48). It has been assumed that the mass transfer of coke precursors from the bulk of the gas to the walls was controlling the rate of deposition (39). Kinetic models (24,49,50) were developed based on the chemical reaction at the wall as a controlling step. Bench-scale data (51—53) appear to indicate that a chemical reaction controls. However, flow regimes of bench-scale reactors are so different from the commercial furnaces that scale-up of bench-scale results caimot be confidently appHed to commercial furnaces. For example. Figure 3 shows the coke deposited on a controlled cylindrical specimen in a continuous stirred tank reactor (CSTR) and the rate of coke deposition. The deposition rate decreases with time and attains a pseudo steady value. Though this is achieved in a matter of rninutes in bench-scale reactors, it takes a few days in a commercial furnace. 

Flow Reactors Fast reactions and those in the gas phase are generally done in tubular flow reaclors, just as they are often done on the commercial scale. Some heterogeneous reactors are shown in Fig. 23-29 the item in Fig. 23-29g is suited to liquid/liquid as well as gas/liquid. Stirred tanks, bubble and packed towers, and other commercial types are also used. The operadon of such units can sometimes be predicted from independent data of chemical and mass transfer rates, correlations of interfacial areas, droplet sizes, and other data. 

Batch Stirred Tanks Tanks agitated by coaxial impellers (turbines, paddles, or propellers) are commonly used for batch dissolution of solids in liquids and may be used for leaching fine solids. Insofar as the controlhng rate in the mass transfer is the rate of transfer of mate-... 

In order to allow integration of countercurrent relations like Eq. (23-93), point values of the mass-transfer coefficients and eqiiilibrium data are needed, over ranges of partial pressure and liquid-phase compositions. The same data are needed for the design of stirred tank performance. Then the conditions vary with time instead of position. Because of limited solubihty, gas/liquid reactions in stirred tanks usually are operated in semibatch fashion, with the liquid phase charged at once, then the gas phase introduced gradually over a period of time. CSTR operation rarely is feasible with such systems. 

A basic stirred tank design is shown in Fig. 23-30. Height to diameter ratio is H/D = 2 to 3. Heat transfer may be provided through a jacket or internal coils. Baffles prevent movement of the mass as a whole. A draft tube enhances vertical circulation. The vapor space is about 20 percent of the total volume. A hollow shaft and impeller increase gas circulation (as in Fig. 23-31). A splasher can be attached to the shaft at the hquid surface to improve entrainment of gas. A variety of impellers is in use. The pitched propeller moves the liquid axially, the flat blade moves it radially, and inclined blades move it both axially and radially. The anchor and some other designs are suited to viscous hquids. 

TABLE 23-12 Correlations of Mass-Transfer Coefficients in Stirred Tanks... 

Two complementai y reviews of this subject are by Shah et al. AIChE Journal, 28, 353-379 [1982]) and Deckwer (in de Lasa, ed.. Chemical Reactor Design andTechnology, Martinus Nijhoff, 1985, pp. 411-461). Useful comments are made by Doraiswamy and Sharma (Heterogeneous Reactions, Wiley, 1984). Charpentier (in Gianetto and Silveston, eds.. Multiphase Chemical Reactors, Hemisphere, 1986, pp. 104—151) emphasizes parameters of trickle bed and stirred tank reactors. Recommendations based on the literature are made for several design parameters namely, bubble diameter and velocity of rise, gas holdup, interfacial area, mass-transfer coefficients k a and /cl but not /cg, axial liquid-phase dispersion coefficient, and heat-transfer coefficient to the wall. The effect of vessel diameter on these parameters is insignificant when D > 0.15 m (0.49 ft), except for the dispersion coefficient. Application of these correlations is to (1) chlorination of toluene in the presence of FeCl,3 catalyst, (2) absorption of SO9 in aqueous potassium carbonate with arsenite catalyst, and (3) reaction of butene with sulfuric acid to butanol. 

A common process task involves heating a slurry by pumping it through a well-stirred tank. It is useful to know the temperature profile of the slurry in the agitated vessel. This information can be used to optimize the heat transfer process by performing simple sensitivity studies with the formulas presented below. Defining the inlet temperature of the slurry as T, and the temperature of the outer surface of the steam coil as U then by a macroscopic mass and energy balance for the system, a simplified calculation method is developed. 

The stirred tank reaetor is often ehosen sinee it ean aehieve an exeellent nearuniform suspension of erystal partieles. The mass transfer eoeffieient in flat interfaee stirred tank is dependent on the stirring rate as (Hikita and Ishikawa, 1969)... 

The mass transfer, KL-a for a continuous stirred tank bioreactor can be correlated by power input per unit volume, bubble size, which reflects the interfacial area and superficial gas velocity.3 6 The general form of the correlations for evaluating KL-a is defined as a polynomial equation given by (3.6.1). 

Various reactor combinations are used. For example, the product from a relatively low solids batch-mass reactor may be transferred to a suspension reactor (for HIPS), press (for PS), or unagitated batch tower (for PS) for finishing. In a similar fashion, the effluent from a continuous stirred tank reactor (CSTR) may be transferred to a tubular reactor or an unagitated or agitated tower for further polymerization before devolatilization. 

Recycling of partially reacted feed streams is usually carried out after the product is separated and recovered. Unreacted feedstock can be separated and recycled to (ultimate) extinction. Figure 4.2 shows a different situation. It is a loop reactor where some of the reaction mass is returned to the inlet without separation. Internal recycle exists in every stirred tank reactor. An external recycle loop as shown in Figure 4.2 is less common, but is used, particularly in large plants where a conventional stirred tank would have heat transfer limitations. The net throughput for the system is Q = but an amount q is recycled back to the reactor inlet so that the flow through the reactor is Qin + q- Performance of this loop reactor system depends on the recycle ratio qlQin and on the type of reactor that is in the loop. Fast external recycle has... 

Membrane Reactors. Consider the two-phase stirred tank shown in Figure 11.1 but suppose there is a membrane separating the phases. The equilibrium relationship of Equation (11.4) no longer holds. Instead, the mass transfer rate across the interface is given by... 

Four mmoles of malononitrile and benzaldehyde were introduced in a batch stirred tank reactor at 323 K with toluene as solvent (30 ml). Then 0.05 g of aluminophosphate oxynitride was added. Samples were analysed by gas chromatography (Intersmat Delsi DI200) using a capillary column (CPSilSCB-25 m). Care was taken to avoid mass or heat transfer limitations. Before the reaction no specific catalyst pretreatment was done. 

Extraction can be performed in stirred tanks if the process proceeds fast and separation of phases is ea.sy, but column extractors are most commonly used. The column can be filled with a particulate material. The liquids flow countercurrently whereby the flow can be uniform or pulsed. Reciprocated and rotary agitators are often used to enhance mass transfer. An example of the latter type is shown in Fig. 7.2-13 (asymmetric rotating disk (ARD) extractor). 

The principle of the perfectly-mixed stirred tank has been discussed previously in Sec. 1.2.2, and this provides essential building block for modelling applications. In this section, the concept is applied to tank type reactor systems and stagewise mass transfer applications, such that the resulting model equations often appear in the form of linked sets of first-order difference differential equations. Solution by digital simulation works well for small problems, in which the number of equations are relatively small and where the problem is not compounded by stiffness or by the need for iterative procedures. For these reasons, the dynamic modelling of the continuous distillation columns in this section is intended only as a demonstration of method, rather than as a realistic attempt at solution. For the solution of complex distillation problems, the reader is referred to commercial dynamic simulation packages. 

The gas-liquid flow characteristics of stirred vessels depend both on the level of agitation and the rate of gas flow and can vary from the case of bubble column type operation to that of a full circulating tank, as shown in Fig. 5.123. The mixing characteristics and gas distribution obtained, obviously exert a considerable influence on the rate of mass transfer obtained (Harnby et al., 1985). 

Chapter 3 concerns the dynamic characteristics of stagewise types of equipment, based on the concept of the well-stirred tank. In this, the various types of stirred-tank chemical reactor operation are considered, together with allowance for heat effects, non-ideal flow, control and safety. Also included is the modelling of stagewise mass transfer applications, based on liquid-liquid extraction, gas absorption and distillation. 

Convection is mass transfer that is driven by a spatial gradient in pressure. This section presents two simple models for convective mass transfer the stirred tank model (Section II.A) and the plug flow model (Section n.B). In these models, the pressure gradient appears implicitly as a spatially invariant fluid velocity or volumetric flow rate. However, in more complex problems, it is sometimes necessary to develop an explicit relationship between fluid velocity and pressure gradients. Section II.C describes the methods that are used to develop these relationships. 

One of the simplest models for convective mass transfer is the stirred tank model, also called the continuously stirred tank reactor (CSTR) or the mixing tank. The model is shown schematically in Figure 2. As shown in the figure, a fluid stream enters a filled vessel that is stirred with an impeller, then exits the vessel through an outlet port. The stirred tank represents an idealization of mixing behavior in convective systems, in which incoming fluid streams are instantly and completely mixed with the system contents. To illustrate this, consider the case in which the inlet stream contains a water-miscible blue dye and the tank is initially filled with pure water. At time zero, the inlet valve is opened, allowing the dye to enter the... 

Figure 2 The stirred tank, a simple model for convective mass transfer. The liquid in the tank is characterized by its volume (V), density (p), and the concentrations of the components (CA). Liquid enters through the inlet stream at a flow rate Qm and concentration CA0. Liquid exits through the outlet stream at volumetric flow rate Qml and concentration identical to that in the tank (CA). The concentration profile below the tank shows the step change in concentration encountered as the inlet stream is mixed with tank contents of lower concentration.

Mass balance equations can be developed to describe mass transfer in the stirred tank. The system is defined as the fluid within the tank, excluding any headspace above the fluid and the solid tank itself. The total mass balance on this sytem, given above in verbal form as Eq. (1), takes the following form when fluid density (p) is assumed to be constant ... 

As with the stirred tank model, mass balance equations can be developed to describe mass transfer in plug flow. In this case, it is convenient to define the system as a differential cylindrical section of the tube, with length Az and volume nD2 Az/4, where D is the tube diameter. This system is fixed in space and may... 

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